203ch18_slides.pdf - STAT 203 Chapter 18 Inferences About...

This preview shows page 1 - 5 out of 20 pages.

STAT 203 Chapter 18 Inferences About Means Recall that we use sample statistics to estimate population parameters. Since the value of a statistic varies from sample to sample, we can use the standard deviation to measure the variability of a statistic. Population parameter Sample statistic Standard deviation of statistic Standard error of statistic Population proportion p Sample proportion ˆ p SD p ) = p (1 - p ) n SE p ) = ˆ p (1 - ˆ p ) n Population mean μ Sample mean y SD ( y ) = σ n SE ( y ) = s n where σ and s are the population standard deviation and the sample standard deviation, respectively. Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 1
Image of page 1

Subscribe to view the full document.

STAT 203 Standard error of the sample mean y : In most situations, the value of the population standard deviation σ is unknown, and hence so is SD ( y ) = σ n . We will estimate σ using the sample standard deviation s from a random sample, and estimate SD ( y ) = σ n by the standard error SE ( y ) = s n . In Chapter 15, the confidence interval for a population proportion p is given by: ˆ p ± z * SE p ) where the critical value z * is based on the standard Normal model. In general, the confidence interval for a population parameter takes the following form: statistic ± critical value × (standard error of statistic) Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 2
Image of page 2
STAT 203 Confidence intervals for the population mean μ When σ is unknown , we’ll use SE ( y ) = s n , and the confidence interval for μ will be based on the t - model instead of the standard Normal model (see Appendix for the theoretical details). A confidence interval of confidence level C for μ is constructed using: y ± t * n - 1 s n where the critical value t * n - 1 can be obtained from the t-table. (See the t-table posted on the course website.) Such a confidence interval for μ is called the one-sample t -interval . Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 3
Image of page 3

Subscribe to view the full document.

STAT 203 Properties of the t -model * perfectly symmetric about the mean 0 * unimodal, bell-shaped * has one model parameter – the degrees of freedom ( df ) which determines the shape of the model and is given by n - 1 * has thicker tails when sample size is smaller *
Image of page 4
Image of page 5

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern